Question 1

How many times in a day, are the hands of a clock in straight line but opposite in direction?

Accepted Answer

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only). So, in a day, the hands point in the opposite directions 22 times.

Question 2

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

Accepted Answer

Angle traced by hour hand in 12 hrs = 360º. Angle traced by hour hand in 5 hrs 10 min. i.e., 31/6 hrs = 360 12 * 31 6 ° = 155º

Question 3

A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?

Accepted Answer

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours. The Watch gains 2 + 4 4 5 min. or 34 5 min.in 170 hrs. Now, 34 5 min.are gained in 170 hrs. 2 min.are gained in 170 * 5 34 * 2 hrs=50 hrs Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday

Question 4

At 3.40, the hour hand and the minute hand of a clock form an angle of:

Accepted Answer

Angle traced by hour hand in 12 hrs. = 360º. Angle traced by it in 11/3 hrs= 360 12 * 11 3 ° = 110 ° Angle traced by minute hand in 60 min. = 360º. Angle traced by it in 40 min. =(360/60*40) ° =240 ° Required angle (240 - 110)º = 130º.

Question 5

Find at what time between 9 and 10 o’clock will the hands of a clock be in 180° ?

Accepted Answer

At 9 o’clock, the hour hand is at 9 and the minutes hand is at 12, i.e., the two hands are 15 min. spaces apart. So, the minute hand should gain = (30 - 15) minutes = 15 minutes 55 minutes will be gained in 60 min. 15 minutes spaces will be gained in ((60/55) x 15) min. = 180/11 min. The hands will be in the same straight line but not together i.e.,in 180 degrees at 180/11 min. past 9.

Question 6

Calculate the angle between the two hands of clock when the clock shows 4 : 20 p.m. ?

Accepted Answer

Since at 4 : 20 the minute hand will be at 4 and the angle between them will be same as the distance covered in degree by the hour hand in 20 minutes. Required angle = distance of hour hand = speed × time = 1 2 × 20 =10 degrees.

Question 7

1 Billion Seconds Equals to

Accepted Answer

We know that 1 year = 365.25 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds => 1 Year = 365.25 x 24 x 60 x 60 Seconds But 1 billion seconds = ? 1 Year = 365.25 x 24 x 60 x 60 Seconds ? = 1000000000 Seconds ? = 1000000000 365 . 25 x 24 x 60 x 60 years = 31. 68 years.

Question 8

Minute hand overlaps hour hand in 65 mins. In how many days it will gain 1440 hours ?

Accepted Answer

In this problem , it has considered that 65 mins = 1hr So mins has increased by 5 mins so multiply 5 x 24 = 120 mins extra , That is now per day it adds 2hr extra, so divide 1440/26 = 59.384 days =~ 60 days.

Question 9

At what time between 2 and 3 O'clock, the hands of a clock coincide ?

Accepted Answer

Since, in one hour, two hands of a clock coincide only once, so, there will be value. Required time T = 2 11 H × 30 + A o minutes past H. Here H - initial position of hour hand = 2 (since 2 O'clock) A° = Required angle = 0° (Since it coincides) T = 2 11 2 × 30 + 0 o minutes past 2 => 1 10 11 minutes past 2

Question 10

The reflex angle between the hands of a clock at 11:35 is ?

Accepted Answer

Apply the formula for finding the angle: Angle=(30h-(11/2)m( where m stands for minutes and h stands for hours) Hence, 30x11 - 11/2x35 = 330 - 192.5 = 137.5 degrees The reflex angle = 360 - 192.5 degree = 222.5 degrees.

Question 11

A clock is started at 11 a.m. By 600 seconds past 6 p.m, the hour hand has turned through ?

Accepted Answer

The total angle traced by the hour hand is the angle traced in 7 hours and 10 minutes. We know that the angle traced by the hour hand in one hour is 30º and in one minute is 1/2º. Therefore, (30º x 7) + (10 x 1/2º) = 215º is the angle traced by the hour hand.

Question 12

There is a clock which shows false timing ie it shows 20 minutes less for each 1 hour. If the clock shows 12 noon now how many minutes will be lost when it shows 2 pm ?

Accepted Answer

For 1 hour, 20 minutes is slower, then for 06 miuntes - 2 minutes is slower 30 minutes - 10 minutes Actual time | false time 12 12 01 PM 12:40 PM (20 minutes slower) 02 PM 01:20 PM 03 PM 02:00 PM So, when actual time is 3pm, the false time is 2 pm. So, it loses 60 minutes when it shows 2 pm.

Question 13

How many minutes is it until 6 o'clock if 50 minutes ago it was 4 times as many minutes past 3 o'clock ?

Accepted Answer

Let the required number of minutes = M Total minutes between 3o'clock and 6o' clock = 180 minutes M + 50 + 4M = 180 5M + 50 = 180 5M = 130 M = 26 minutes.

Question 14

If a Siren sounds for every 5 seconds, how many times will it sound in ¾ of an hour?

Accepted Answer

There are 60 minutes in an hour. In ¾ of an hour there are (60 × ¾) minutes = 45 minutes. In ¾ of an hour there are (60 × 45) seconds = 2700 seconds. Siren sounds for every 5 seconds. In 2700 seconds = 2700/5 = 540 times. The count start after the first sound, the Siren will sound 541 times in ¾ of an hour.

Clock Puzzles Questions